1. Field of the Invention
The present invention relates to a digital hyperbolic function generator which generates a hyperbolic function of polygonal line approximation with time as a variable.
2. Description of the Prior Art
Prior art, well-known hyperbolic function generators include an analog type apparatus which utilizes forward characteristics of diodes and which comprises an operational amplifier and several diodes connected to an input of the operational amplifier and having their forward conduction potentials set to different values with respect to an input voltage by dividing resistors. By appropriately selecting the settings of the conduction potentials of the diodes an output voltage which is in hyperbolic function relation with the input voltage can be polygonal line approximated, with the conduction potentials of the diodes being junction points of the polygonal line.
The above analog hyperbolic function generator, however, has a drawback in that it is difficult to provide a function generator of constant characteristic because of mismatching in the diode characteristics and the adjustment of the generator is difficult. Further, operation is unstable because of the temperature dependency of the diodes and the resistors.
Now considering a hyperbolic function y = K/x (where K is a constant) shown in FIG. 1, as the variable x increment increases only by a fixed amount x.sub.o such that x.sub.o, 2x.sub.o, 3x.sub.o, . . . , nx.sub.o (where n is an integer) the function y changes to K/x.sub.o, K/2x.sub.o, K/3x.sub.o, . . . , K/nx.sub.o. The polygonal line (shown by dotted line) obtained by connecting the points A.sub.1, A.sub.2, A.sub.3, A.sub.4, A.sub.5, A.sub.6, A.sub.7 and A.sub.8 is an approximation of the hyperbolic function y = K/x. It is seen that when the gradient of the segment A.sub.1 A.sub.2 is assumed to be 1, then the gradients of the respective segments form a progression of 1, 1/3, 1/6, 1/10, 1/15, 1/21, 1/28, 1/36. It is apparent that the smaller the constant amount x.sub.o is the more is the approximation enhanced.